Resizable child elements does not maintain minimum width and height when resizing parent

Resizable child elements does not maintain minimum width and height when resizing parent

var resizable = function(that){
var resizeSelector = '#'+that.attr('id')+' .resize';
that.addClass("resize"); // Adding dummy class 'resize' to select resizable child elements using the above selector.
that.resizable({
    alsoResize: resizeSelector,
    maxHeight: 600,
   maxWidth:600,
   minHeight: 35,
   minWidth:35
    })
};

The child elements are given the above resizable attributes. Resizing beyond the minimum width of the child element is not restrained when resizing the parent div. 

Thanks,
Jim